Chapter 8.10, Problem 4CYU

(a)

To determine

The system of equations of:

Amanda pays an annual fee of $\$100$ to belong to a gym plus a monthly fee of $\$10$ . Maria pays only a monthly fee of $\$20$ .

Answer to Problem 4CYU

The system of equation is written as:

  $\begin{array}{l}y=10x+100\\ y=20x\end{array}$

Explanation of Solution

Given:

Amanda pays an annual fee of $\$100$ to belong to a gym plus a monthly fee of $\$10$ .

Maria pays only a monthly fee of $\$20$ .

Calculation:

The equation is written as:

  $y=10x+100$  .... (1)

  $y=20x$  .... (2)

Conclusion:

The system of equation is written as:

  $\begin{array}{l}y=10x+100\\ y=20x\end{array}$

(b)

To determine

The solution of the system by using the graphing method and meaning of the solution is to be needed.

Answer to Problem 4CYU

  

Explanation of Solution

Given:

Amanda pays an annual fee of $\$100$ to belong to a gym plus a monthly fee of $\$10$ .

Maria pays only a monthly fee of $\$20$ .

Calculation:

The equation is written as:

  $y=10x+100$  .... (1)

  $y=20x$  .... (2)

Now, draw a graph these two eqns.

  

From graph:

Notice that they have an intersection at $\left(10,200\right)$

This would mean that $10$ months, both would have the same cost at $200$ dollars.

Conclusion:

So, by using the graphing method the solution of the system of equations is $\left(10,200\right)$ which is point of intersection.